System and method for imaging properties of subterranean formations

ABSTRACT

A system and method for imaging properties of subterranean formations in a wellbore is provided. The system comprises a formation sensor for collecting currents injected into the subterranean formations, the formation sensor positionable on a downhole tool deployable into the wellbore. The system comprises a controller for controlling the formation sensor and a formation imaging unit. The formation imaging unit comprises a current management unit for collecting data from the currents injected into the subterranean formations, the currents having at least two different frequencies. The formation imaging unit comprises a drilling mud data unit for determining at least one drilling mud parameter, a formation data unit for determining at least one formation parameter from the collected data, and an inversion unit for determining at least one formation property by inverting the at least one formation parameter.

TECHNICAL FIELD

The present invention relates to techniques for performing wellboreoperations. More particularly, the present invention relates totechniques for determining characteristics of subterranean formations.

BACKGROUND

Oil rigs are positioned at wellsites for performing a variety ofoilfield operations, such as drilling a wellbore, performing downholetesting and producing located hydrocarbons. Downhole drilling tools areadvanced into the earth from a surface rig to form a wellbore. Drillingmuds are often pumped into the wellbore as the drilling tool advancesinto the earth. The drilling muds may be used, for example, to removecuttings, to cool a drill bit at the end of the drilling tool and/or toprovide a protective lining along a wall of the wellbore. During orafter drilling, casing is typically cemented into place to line at leasta portion of the wellbore. Once the wellbore is formed, production toolsmay be positioned about the wellbore to draw fluids to the surface.

During drilling, measurements are often taken to determine downholeconditions. In some cases, the drilling tool may be removed so that awireline testing tool may be lowered into the wellbore to takeadditional measurements and/or to sample downhole fluids. Once thedrilling operation is complete, production equipment may be lowered intothe wellbore to assist in drawing the hydrocarbons from a subsurfacereservoir to the surface.

The downhole measurements taken by the drilling, testing, productionand/or other wellsite tools may be used to determine downhole conditionsand/or to assist in locating subsurface reservoirs containing valuablehydrocarbons. Such wellsite tools may be used to measure downholeparameters, such as temperature, pressure, viscosity, resistivity, etc.Such measurements may be useful in directing the oilfield operationsand/or for analyzing downhole conditions.

Attempts have been made to measure certain characteristics of awellbore. Various techniques have been developed for measuring downholeparameters as described, for example, in US Patent/Application Nos.20090204346, 20090153155, 20090072833, 20090090176, 20080288171,7,689,363, 7,394,258, 7,397,250, 7,258,005, 5,457,396, 6,527,923,7,066,282, 6,801,039, 5,677,631, 5,574,371, 5,345,179, 6,191,588,3,879,644, 3,816,811, 4,608,983, 4,567,759, and 7,689,363. Techniqueshave also been developed for scanning as stated in publications“Formation Imaging with Microelectrical Scanning Arrays”, and “A GeneralFramework for Constraint Minimization for the Inversion ofElectromagnetic Measurements.”

More specifically, European Patent Application Nos. 102900084.2 and10290083.4, filed by Applicant and incorporated herein by reference,relate to techniques for determining electrical parameters of downholefluids.

In addition, International Patent Application No. PCT/EP2009/007637,filed by Applicant and incorporated herein by reference, relates to atool and method for imaging a formation through a substantiallynon-conductive medium. The tool comprises a first circuitry forinjecting a current into the formation, wherein a complex impedance tothe current is measured. A second circuitry for determining a phaseangle of an impedance of the nonconductive medium and a third circuitryfor determining a component of the complex impedance that is orthogonalto the phase angle.

Despite the development of techniques for measuring downhole parameters,there remains a need to provide advanced techniques for determiningparameters of downhole formations and/or wellbore fluids. It may bedesirable to provide techniques that enhance downhole fluid and/ordownhole formation measurements. It may be further desirable to providetechniques that correct for the effects of mud on downhole imagingand/or measurement. Preferably, such techniques involve one or more ofthe following, among others: accuracy of measurements, optimizedmeasurement processes, operability in a variety of downhole fluids suchas conductive and non-conductive muds, flexible measurement and/oranalysis, operability in downhole conditions (e.g., at high temperaturesand/or pressures), etc.

DISCLOSURE OF THE INVENTION

The present invention relates to a formation imaging unit for imagingproperties of at least one subterranean formation in a wellbore at awellsite. The formation imaging unit comprises a current management unitfor collecting data from at least two currents injected into the atleast one subterranean formation, the at least two currents having atleast two different frequencies, and a drilling mud data unit fordetermining at least one drilling mud parameter. The formation imagingunit comprises a formation data unit for determining at least oneformation parameter from the collected data, and an inversion unit fordetermining at least one formation property by inverting the at leastone formation parameter.

The present invention relates to a system for imaging properties of atleast one subterranean formation in a wellbore at a wellsite. The systemcomprises a formation sensor for collecting at least two currentsinjected into the at least one subterranean formation, the formationsensor positionable on a downhole tool deployable into the wellbore, acontroller for controlling the formation sensor, and a formation imagingunit. The formation imaging unit comprises a current management unit forcollecting data from the at least two currents injected into the atleast one subterranean formation, the at least two currents having atleast two different frequencies. The formation imaging unit comprises adrilling mud data unit for determining at least one drilling mudparameter, a formation data unit for determining at least one formationparameter from the collected data, and an inversion unit for determiningat least one formation property by inverting the at least one formationparameter.

The present invention relates to a method for imaging properties of atleast one subterranean formation in a wellbore at a wellsite. The methodcomprises deploying a downhole tool into the wellbore, the downhole toolhaving a formation sensor thereon and collecting at least two currentssent through the at least one subterranean formation from the formationsensor. The method comprises sending formation data from the at leasttwo currents to a formation imaging unit. The formation imaging unitcomprises a current management unit for collecting data from the atleast two currents injected into the at least one subterraneanformation, the at least two currents having at least two differentfrequencies, a drilling mud data unit for determining at least onedrilling mud parameter, a formation data unit for determining at leastone formation parameter from the collected data, and an inversion unitfor determining at least one formation property by inverting the atleast one formation parameter. The method comprises determining at leastone formation property with the formation imaging unit.

BRIEF DESCRIPTION OF THE DRAWINGS

The present embodiments may be better understood, and numerous objects,features, and advantages made apparent to those skilled in the art byreferencing the accompanying drawings. These drawings are used toillustrate only typical embodiments of this invention, and are not to beconsidered limiting of its scope, as the invention may admit to otherequally effective embodiments. The figures are not necessarily to scaleand certain features and certain views of the figures may be shownexaggerated in scale or in schematic in the interest of clarity andconciseness.

FIG. 1 is a schematic view of a system for imaging properties of one ormore subterranean formations having a downhole tool deployable into awellbore.

FIG. 2 is a schematic view of the downhole tool of FIG. 1 depicting thedownhole tool with a sensor pad having a formation sensor thereon.

FIG. 3 is a longitudinal cross-sectional view of the sensor pad of FIG.2 taken along line A-A depicting the formation sensor on a face of thesensor pad.

FIG. 4 is a longitudinal cross-sectional view of an alternate sensor padof FIG. 3.

FIG. 5 depicts a schematic diagram illustrating a formation imagingunit, wherein the formation imaging unit is for imaging properties of atleast one subterranean formations at the wellsite.

FIGS. 6-11 are graphical depictions of various outputs created by theformation imaging unit of FIG. 5.

FIG. 12 is a flow chart depicting a method of imaging properties of atleast one subterranean formation.

FIG. 13A is an example image of mud sensor impedance measured at twofrequencies in a well filled with oil-based mud using the imaging unitor system described herein.

FIG. 13B is an image obtained after inversion of impedance shown in FIG.13A.

DESCRIPTION OF EMBODIMENT(S)

The description that follows includes exemplary apparatus, methods,techniques, and instruction sequences that embody techniques of thepresent inventive subject matter. However, it is understood that thedescribed embodiments may be practiced without these specific details.Presently preferred embodiments of the invention are shown in theabove-identified Figures and described in detail below.

FIG. 1 is a schematic view of a wellsite 100 having an oil rig 102 witha downhole tool 104 suspended into a wellbore 106 therebelow. Thewellbore 106 has been drilled by a drilling tool (not shown). A drillingmud, and/or a wellbore fluid 108, may have been pumped into the wellbore106 and may line a wall thereof. As shown, a casing 110 has also beenpositioned in the wellbore 106 and cemented into place therein. Thedownhole tool 104 may have one or more sensors for determining one ormore downhole parameters, such as wellbore fluid parameters and/orformation parameters. The downhole tool 104 may communicate with acontroller 112, a communication network 114 and/or one or more offsitecomputers 116. The downhole tool 104, the controller 112, thecommunication network 114 and/or the offsite computers 116 may have aformation imaging unit 118. The fluid parameters and/or the formationparameters sensed by the downhole tool 104 may be sent to the formationimaging unit 118 to determine formation properties and/or to optimize awell plan at the wellsite 100. The term “imaging” as used herein, is acommon term in the geophysics and oilfield art to refer to arepresentation that depicts an array of localized properties of awellbore in two or more dimensions.

The downhole tool 104 is shown as a wireline logging tool lowered intothe wellbore 106 to take various measurements. The downhole tool 104 mayinclude a conventional logging device 119, one or more sensor pads 120,one or more telemetry devices 122, and an electronics package 124. Theconventional logging device 119 may be provided with various sensors,measurement devices, communication devices, sampling devices and/orother devices for performing wellbore operations. For example, as thedownhole tool 104 is lowered, it may use devices, such as resistivity orother logging devices, to measure formation parameters and/or downholefluid parameters. The formation parameters and/or the downhole fluidparameters may be the collected data regarding the formation and/or thedownhole fluid. The formation imaging unit 118 may manipulate theformation parameters and optionally the downhole fluid parameters todetermine formation properties and/or downhole fluid properties forexample resistivity.

As shown, the downhole tool 104 may be conveyed into the wellbore 106 ona wireline 126. Although the downhole tool 104 is shown as beingconveyed into the wellbore 106 on a wireline 126, it should beappreciated that any suitable conveyance may be used, such as a slickline, a coiled tubing, a drill string, a casing string and the like. Thedownhole tool 104 may be operatively connected to the controller 112 forcommunication therebetween. The downhole tool 104 may be wired via thewireline 126, as shown, and/or wirelessly linked via the one or moretelemetry devices 122. The one or more telemetry devices 122 may includeany telemetry devices, such as electromagnetic devices, for passingsignals to the controller 112 as indicated by communication links 128.Further, it should be appreciated that any communication device orsystem may be used to communicate between the downhole tool 104 and thecontroller 112. Signals may be passed between the downhole tool 104, thecontroller 112, the communication network 114, and/or the offsitecomputer(s) 116 and/or other locations for communication therebetween.

While the downhole tool 104 is depicted as the wireline tool having theone or more sensor pads 120 thereon, it will be appreciated that the oneor more sensor pads 120 may be positioned downhole on a variety of oneor more tools. For example, the one or more sensor pads 120 may beplaced on any downhole system and/or tool for example, on a drillingstring, a logging while drilling tool (LWD), a measurement whiledrilling tool (MWD), a coiled tubing, a drill stem tester, a productiontubing, a casing, a pipe, or any other suitable downhole tool. Althoughonly one of the one or more sensor pads 120 is shown, it should beappreciated that one or more sensor pads 120 and/or portions of the oneor more sensor pads 120 may be located at several locations in thewellbore 106. The one or more sensor pads 120 are preferably positionedabout an outer surface of the downhole tool 104 so that the wellborefluid 108 may pass therealong for measurement thereof. However, it willbe appreciated that the one or more sensor pads 120 may be positioned atvarious locations about the wellsite 100 as desired for performing fluidand/or formation measurements.

The electronics package 124 may include any components and/or devicessuitable for operating, monitoring, powering, calculating, calibrating,and analyzing components of the downhole tool 104. Thus, the electronicspackage 124 may include a power source, a processor, a storage device, asignal conversion (digitizer, mixer, amplifier, etc.), a signalswitching device (switch, multiplexer, etc.), a receiver device and/or atransmission device, and the like. The electronics package 124 may beoperatively coupled to the one or more sensor pads 120 and/or theformation imaging unit 118. The power source may be supplied by thewireline 126. Further, the power source may be in the electronicspackage 124. The power source may apply multiple currents to the one ormore sensor pads 120. The power source may be provided by a batterypower supply or other conventional means of providing power. In somecases, the power source may be an existing power source used in thedownhole tool 104. The power source may be positioned, for example, inthe downhole tool 104 and wired to the one or more sensor pads 120 forproviding power thereto as shown. Optionally, the power source may beprovided for use with the one or more sensor pads 120 and/or otherdownhole devices. Although the electronics package 124 is shown as oneseparate unit from the one or more sensor pads 120 and/or the formationimaging unit 118, it should be appreciated that any portion of theelectronics package 124 may be included within the one or more sensorpads 120 and/or the formation imaging unit 118. Further, the componentsof the electronics package 124 may be located at various locations aboutthe downhole tool 104, the controller 112 and/or the wellsite 100. Theone or more sensor pads 120 may also be wired or wirelessly connected toany of the features of the downhole tool 104, the formation imaging unit118, the communication network 114, and/or the controller 112, such ascommunication links, processors, power sources or other featuresthereof.

The downhole fluid 108, or wellbore fluid, or borehole mud fluid, usedat the wellsite 100 may be an oil-based drilling mud. The downhole fluid108 may be pumped into the wellbore 106 during drilling and/or otherdownhole operations. The downhole fluid 108 may coat a wellbore wall 130as it encounters the wellbore wall 130. The downhole fluid 108 coated onthe wellbore wall 130 may form a mud cake 132, or mud standoff. The mudcake 132 may create a gap 134, or standoff, or mud standoff, or sensorstandoff, between the one or more sensor pads 120 and a subterraneanformation 136. Further roughness of the wellbore wall 130 may cause thegap 134, or standoff, or sensor standoff, between the one or more sensorpads 120 and the subterranean formation 136. The oil-based drilling mudmay have a high resistivity. For example, the resistivity of awater-based drilling mud may be between 0.01-20 Ohm and the resistivityfor the oil-based drilling mud may be 10,000 to 10,000,000 times higherthan the water-based drilling mud. Due to the high resistivity of theoil-based drilling mud, the properties of the oil-based drilling mudmust be accounted for when determining formation properties, as will bediscussed in more detail below. Because the same downhole fluid 108, ordrilling mud, is typically used during wellsite operation, theproperties of the downhole fluid 108 may remain relatively constantalong the length of the wellbore 106.

The one or more sensor pads 120 may be capable of determining one ormore downhole fluid parameters and/or one or more formation parameters.The one or more sensor pads 120 may determine the downhole parameters ofthe downhole fluids 108 and/or the subterranean formations 136 as thedownhole tool 104 passes through the wellbore 106. As shown, the one ormore sensor pads 120 may be positioned on an outer surface 138 of thedownhole tool 104. A portion of the one or more sensor pads 120 may berecessed a distance below the outer surface 138 to provide additionalprotection thereto, or protruded a distance therefrom to access fluidand/or subterranean formation 136. The one or more sensor pads 120 mayalso be positioned at various angles and locations as desired.

FIG. 2 shows a schematic view of the downhole tool 104 located in thewellbore 106 and within the subterranean formation 136. As depicted, thedownhole tool 104 is a wireline microresistivity tool containing the oneor more sensor pads 120 with a formation sensor 200 and optionally a mudsensor 202. The one or more sensor pads 120 may be located on the outersurface 138, or located on one or more arms 204 which extend fromdownhole tool 104. The one or more arms 204 may be configured to placethe one or more sensor pads 120 as close to the wellbore wall 130, oragainst the mud cake 132 on the wellbore wall 130, as possible. The oneor more arms 204 may be actuatable, or spring loaded in order to locatethe one or more sensor pads 120 against the wellbore wall 130.

The formation sensor 200 may be any sensor configured to determine oneor more formation parameters. The formation sensor 200 may send, orinject, a plurality of currents through a portion of the subterraneanformation 136 between two electrodes. The plurality of currents may havetwo or more frequencies, as will be discussed in more detail below. Theplurality of currents may pass through the downhole fluid 108 and thesubterranean formation 136. The injected current may include informationregarding formation and/or fluid parameters. The current detected by theformation sensor 200 may be sent to the formation imaging unit 118. Theformation and/or fluid parameters may be manipulated by the formationimaging unit 118 to determine one or more formation properties, as willbe discussed in more detail below. When the downhole fluid 108 is theoil-based drilling mud, the impedance contribution from the mud cake 132may be significantly larger than the impedance contribution from theformation 136.

The mud sensor 202 may be an optional sensor configured to determine oneor more downhole fluid parameters. The mud sensor 202 may be configuredto send, or inject, current through the downhole fluid 108 and/or themud cake 132. The current injected and detected by the mud sensor 202may have the same frequencies as the plurality of currents injected bythe formation sensor 200. The current detected by the mud sensor 202 maybe sent to the formation imaging unit 118.

FIG. 3 depicts a cross sectional view of the sensor pad 120 of FIG. 2having the formation sensor 200 and the mud sensor 202. As shown, theformation sensor 200 may have one or more source electrodes 300 and oneor more return electrode 302 connected to the electronics package 124.The electronics package 124 may send a plurality of currents 304A to thesource electrode 300. The plurality of currents 304A may travel throughthe mud cake 132, through the subterranean formation 136 and into thereturn electrode 302. The return electrode 302 may send the collectedplurality of currents 304A to the electronics package 124 and/or theformation imaging unit 118.

The sensor pad 120 may optionally have the mud sensor 202. The mudsensor 202 may be configured to send a plurality of currents 304Bthrough the mud cake 132 and/or the downhole fluid 108 (as shown in FIG.1). By sending the plurality of currents 304B through the mud cake 132and/or downhole fluid 108 only, the downhole fluid parameters may bedetermined. The mud sensor 202 may have the one or more sourceelectrodes 300 and a mud return electrode 306. The electronics package124 may send the plurality of currents 304B to the mud sensor 202, andsource electrodes 300. The mud sensor 202, as shown, has a recessedconfiguration. The recessed configuration may be configured to pass theplurality of currents 304B through a fluid zone 308. The mud returnelectrode 306 may send the collected plurality of currents 304B to theelectronics package 124 and/or the formation imaging unit 118.

FIG. 4 depicts a cross sectional view of an alternated sensor pad 120 ofFIG. 2 having the formation sensor 200 and the mud sensor 202. Theformation sensor 200, as shown, may be located proximate a face 400 ofthe pad in a similar manner as shown in FIG. 3. The mud sensor 202;however, may be located on a side surface 402 of the sensor pad 120.Locating the mud sensor 202 on the side surface 402 may allow theplurality of currents 304B sent from the source electrodes 300 to themud return electrode 306 to pass only through the downhole fluid 108. Ina similar manner, as described herein, the return electrode 302 and themud return electrode 306 may send the collected plurality of currents304A and/or 304B to the electronics package 124 and/or the formationimaging unit 118. Although the mud sensor 202 is shown as being arecessed sensor, or a sensor on the side surface 402 of the sensor pad120, it should be appreciated that the mud sensor 202 may be anysuitable sensor for determining the downhole fluid parameters. The mudsensor 202 may also pass the plurality of current 304B through theformation 136. Further, the formation sensor 200 may be any suitablesensor for determining formation and/or downhole fluid parameters.

The plurality of currents 304A and/or 304B may be high frequency currentin order to penetrate the highly resistive oil-based drilling mud. Dueto the high frequency of the plurality of currents 304A and/or 304B, thesource electrodes 300 and the return electrode 302 and/or the mud returnelectrode 306 may be located in close proximity to one another, as shownin FIGS. 3 and 4. The frequency range of the formation sensor 200 and/orthe mud sensor 202 may be optimized in a frequency range from a fewhundred KHz up to roughly 100 Mhz. Due to the frequency, the formationsensor 200 and/or the mud sensor 202 may be adapted to the full range ofoil-based-mud micro-resistivity imaging tools such as OBMI, as shown inU.S. Pat. No. 6,191,588, which is herein incorporated by reference inits entirety. Thus, the downhole tool 104 (as shown in FIG. 2A) maymeasure the downhole fluid 108 at the same, or similar, frequency orfrequencies as the subterranean formation 136.

The source electrodes 300, the return electrodes 302, and the mud returnelectrode 306 may be any conventional electrode capable of generatingthe plurality of currents 304A and/or 304B across the oil-based drillingmud, or downhole fluid 108. A power source (e.g., included in theelectronics package 124 of FIG. 1) may be operatively connected to thesource and return electrodes 300/302 for applying a voltage (V+, V−)thereacross. As voltage is applied, a plurality of currents 304A/304Bthat may flow out of one of the electrodes 300/302, for example thesource electrodes 300 that can be measured by the return electrodes 302and/or the mud return electrode 306. The source electrodes 300 and thesensor electrodes may be geometrically and materially optimized to matchsubstantially to a fixed characteristic impedance transmission line.

The current from the electrodes may be used to determine variousparameters. In an example involving a fluid passing between a pair ofelectrodes, an AC voltage V is applied between two electrodes togenerate a resultant current I that can be measured at the sensorelectrode, for example the return electrode 302 or the mud returnelectrode 306. The complex impedance Z may be determined from themeasured current based on the following:z=|z|exp(iφhd z)  Equation (1)where its magnitude|z| based on Ohms law and phase φ_(z) are defined asfollows:|z|=|V/I|  Equation (2)φ_(z)=phase of I relative V  Equation (3)and where exp (φ_(z)) based on Euler's formula is defined as follows:exp(iφ _(z))=cos φ_(z) +i sin φ_(z)  Equation (4)The magnitude and phase of the impedivity (sometimes referred to as thecomplex impedivity) of a fluid ζ is defined as follows:ζ=|ζ|exp(iφ _(ζ))  Equation (5)Equation (5) may be derived from z when the fluid is measured by the mudsensor 202 by the relations as follows:|ζ|=k|z|  Equation (6)Equation (6) may also be written as follows:|ζ|=k|V|/|I|  Equation (7)The phase (or dielectric angle) of the fluid ζ is derived as follows:φ_(ζ)=φ_(z)  Equation (8)where:

-   -   |ζ| is the magnitude of impedivity,    -   φ_(ζ) is the phase angle of the impedivity, and    -   k is a constant for the device.

The constant k may be measured empirically, for example, by measuringthe impedance V/I between electrodes as a fluid of known impedivity. Theconstant k may also be calculated from the geometry of the electrodesusing conventional methods.

Data concerning the measured current may be used to determine fluidparameters, such as impedivity, resistivity, impedance, conductivity,complex conductivity, complex permittivity, tangent delta, andcombinations thereof, as well as other parameters of the downhole fluid108. The data may be analyzed to determine characteristics, orproperties, of the wellbore fluid 108, such as the type of fluid (e.g.,hydrocarbon, mud, contaminants, etc.) The formation imaging unit 118 maybe used to analyze the data, as will be discussed in more detail below.Such analysis may be performed with other inputs, such as historical ormeasured data about this or other wellsites. Reports and/or otheroutputs may be generated from the data. The data may be used to makedecisions and/or adjust operations at the wellsite. In some cases, thedata may be fed back to the wellsite 100 for real-time decision makingand/or operation.

FIG. 5 depicts a block diagram illustrating the formation imaging unit118 of FIG. 1. The formation imaging unit 118 may be incorporated intoor about the wellsite 100 (on or off site) for operation with thecontroller 112. The formation imaging unit 118 may determine, generate,and/or model various formation properties. For example, the formationimaging unit 118 may use an inversion for borehole imaging with amulti-frequency approach. The formation imaging unit 118 may invert forthe formation resistivity, the formation permittivity, and optionallythe mud standoff to determine formation properties. The formationproperties may be used to produce a formation model.

The formation imaging unit 118 may take the form of an entirely hardwareembodiment, an entirely software embodiment (including firmware,resident software, micro-code, etc.), or an embodiment combiningsoftware and hardware aspects. Embodiments may take the form of acomputer program embodied in any medium having computer usable programcode embodied in the medium. The embodiments may be provided as acomputer program product, or software, that may include amachine-readable medium having stored thereon instructions, which may beused to program a computer system (or other electronic device(s)) toperform a process. A machine readable medium includes any mechanism forstoring or transmitting information in a form (such as, software,processing application) readable by a machine (such as a computer). Themachine-readable medium may include, but is not limited to, magneticstorage medium (e.g., floppy diskette); optical storage medium (e.g.,CD-ROM); magneto-optical storage medium; read only memory (ROM); randomaccess memory (RAM); erasable programmable memory (e.g., EPROM andEEPROM); flash memory; or other types of medium suitable for storingelectronic instructions. Embodiments may further be embodied in anelectrical, optical, acoustical or other form of propagated signal(e.g., carrier waves, infrared signals, digital signals, etc.), orwireline, wireless, or other communications medium. Further, it shouldbe appreciated that the embodiments may take the form of handcalculations, and/or operator comparisons. To this end, the operatorand/or engineer(s) may receive, manipulate, catalog and store the datafrom the downhole tool 104 in order to perform tasks depicted in theformation imaging unit 118.

The formation imaging unit 118 may include a storage device 502, acurrent management unit 504, a drilling mud data unit 506, a formationdata unit 508, an inversion unit 510, a formation model unit 512, awellbore optimizer unit 514, an analyzer unit 516, and a transceiverunit 518. The storage device 502 may be any conventional database orother storage device capable of storing data associated with thewellsite 100, shown in FIG. 1. Such data may include, for examplecurrent frequencies, current time and/or location sent, downhole fluidparameters, formation parameters, downhole fluid properties, formationproperties, historical data, formation models, and the like. Theanalyzer unit 516 may be any conventional device, or system, forperforming calculations, derivations, predictions, analysis, andinterpolation, such as those described herein. The transceiver unit 518may be any conventional communication device capable of passing signals(e.g., power, communication) to and from the formation imaging unit 118.The current management unit 504, a drilling mud data unit 506, aformation data unit 508, an inversion unit 510, a formation model unit512, and a wellbore optimizer unit 514 may be used to receive, collectand catalog data and/or to generate outputs as will be described furtherbelow. Portions or the entire formation imaging unit 118 may be locatedabout the wellsite 100 (as shown in FIG. 1).

The current management unit 504 may be configured to generate andcollect the appropriate number and frequency of the plurality ofcurrents 304A and/or 304B, depending on the wellbore 106 conditionsand/or the type of sensor pad 120 used. The number of frequencies usedmay depend on the number of formation parameters and/or downhole fluidparameters to be calculated using the inversion unit 510. The number ofcurrents and frequencies used may be dependent on the downhole fluid 108(as shown in FIG. 1) being measured in-situ, or alternatively calculatedusing an inversion. If the sensor pad 120, downhole tool 104 and/or aseparate downhole tool (not shown) have the mud sensor 202 (as shown inFIGS. 2-4) then the number of the plurality of currents 304A sent intothe formation may be minimized at two logging frequencies. If the mudsensor 202 is not present, the mud properties will be inverted for andwill require the current management unit 504 to generate the pluralityof currents 304A at a minimum of three logging frequencies. The numberof logging frequencies used may increase to improve accuracy and/or asthe number of unknowns in the downhole fluid and/or the formationincrease, as will be described in more detail below.

The current management unit 504 may send the determined number ofmultiple logging frequencies into the formation at substantially thesame time at multiple locations along the formation. The plurality ofcurrents 304B for measuring the downhole fluid properties may have thesame logging frequencies, or a portion of the logging frequencies, asthose sent into the subterranean formation 136 (as shown in FIG. 1). Thecurrent management unit 504 may collect, catalog, store and/ormanipulate current data regarding the logging frequencies sent andcollected by the formation sensor 200 and/or the mud sensor 202 (asshown in FIG. 2). A historical record of the current data may be keptfor each logging location in the wellbore 106 (as shown in FIG. 1).

The drilling mud data unit 506 may be used to collect, catalog, store,manipulate and/or supply mud data. The mud data may be the measured datafrom the mud sensor 202 (as shown in FIG. 2). Further, the mud data maybe obtained from the measured data from the formation sensor 200, whenthere is no separate mud sensor 202. If there is no separate mud sensor202, the mud data may be inverted along with formation data to determinethe downhole fluid properties, as will be discussed in more detailbelow. The measured mud data may be measured mud parameters, or mudelectric parameters, that may be manipulated by the inversion unit 510to determine mud and/or formation properties. The mud data, or mudparameters, may be mud impedance, permittivity, resistivity, and mudstandoff. This mud data that is measured may be manipulated to determinemud properties such as mud permittivity, current amplitude, currentphase, resistivity and conductivity. The downhole fluid propertiestypically do not change significantly in the wellbore 106. Therefore, itmay only be necessary to measure or invert for the mud parametersperiodically at a much lower sampling rate than obtaining the formationparameters. The downhole fluid parameters, or properties, may bedetermined by the one or more sensors independent of a determination ofthe formation parameters. Thus, the determined fluid parameters may beused to more accurately determine the formation parameters as will bedescribed in more detail below.

The formation data unit 508 may be used to collect, catalog, store,manipulate and/or supply formation data. The formation data may be themeasured data from the formation sensor 200 (as shown in FIG. 2).Because the plurality of currents 304A (as shown in FIGS. 3 and 4) mayhave data regarding the mud and the formation, the formation data mayhave to be manipulated in order to determine the formation parametersand/or formation properties. The formation data, or formationparameters, may be the measured parameters from the formation 136 suchas formation impedance, amplitude and phase of the current, and thelike. The formation data, or formation parameters, may be manipulatedalong with the mud data to determine formation properties such asresistivity, conductivity, permittivity, and the like. The formationdata may be obtained from the plurality of currents 304A (as shown inFIGS. 3 and 4) at the plurality of frequencies. The formation data mayhave current data from a plurality of locations along the wellbore 106.

The inversion unit 510 may obtain the formation data and mud data fromthe drilling mud data unit 506 and/or the formation data unit 508. Todetermine formation resistivity, or an inverted formation resistivity,the inversion unit 510 may invert, or parametrically invert, themultiple current measurements made at several frequencies, as will bedescribed in more detail below. The number of frequencies used maydepend on the number of parameters to be inverted. The inversion unit510 may invert the mud data and/or the formation data in order todetermine formation properties and/or downhole fluid properties. Theinverted formation data, and optionally, the mud data, obtained at theplurality of frequencies may be used to obtain formation properties forborehole imaging. The parameters to be inverted may be the formationresistivity, the formation permittivity, and/or the mud standoff (if themud data is collected independently of the formation data). If the mudparameters are not measured, for example, by the mud sensor 202 (asshown in FIG. 2), the downhole fluid properties may be inverted for byadding extra frequencies to the plurality of current 304A used by theformation sensor 200. The inversion unit 510 may further invert signalbiases caused by systematic measurement drifts in the in-phase andout-of-phase signals or in the phase and amplitude signals.

The plurality of currents 304A (as shown in FIGS. 3 and 4) may firstpass through the mud cake 132, or mud-standoff, then the formation. Theimpedance from the mud cake 132 and the formation combined may bemeasured. The measured impedance may be given approximately as:

$\begin{matrix}{Z = {{V/I} = {{K_{mud}\Delta\frac{R_{mud}}{1 + {{j\omega ɛ}_{0}ɛ_{mud}R_{mud}}}} + {K_{rock}\frac{R_{rock}}{1 + {{j\omega ɛ}_{0}ɛ_{rock}R_{rock}}}}}}} & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$

Where Δ is the mud standoff, K_(mud) and K_(rock) are tool relatedcoefficients, and ω is the operating frequency, or logging frequency foreach of the plurality of currents 304A. ∈_(mud) and ∈_(rock) may be therelative permittivity of the mud and the formation respectively. R_(mud)and R_(rock) may be the resistivity of the mud and the formationrespectively. The term ∈₀ represents the permittivity of free space (aconstant=8.85419×10⁻¹²) and j represents √{square root over (−1)}. Theterms subscripted by “mud” represent the contribution to Z from the mudor mudcake occupying the space between the padface and the formation,depending of the electrical properties of the formation, the properties∈_(rock) and R_(rock) the contribution from the mud or mud cake 132 maybe significantly larger than the contribution from the formation.

In equation 9, the formation sensor 200 (as shown in FIGS. 2-4) currentI may have independent components that are respectively in-phase andout-of-phase with the voltage V. These may be its real and imaginaryparts real(I) and imag(I). Therefore, equation 9 may represent twoindependent equations:real(V/I)=ΔK _(mud) R _(mud)/[1+(ω∈_(o)∈_(mud) R _(mud))² ]+K _(rock) R_(rock)/[1+(ω∈_(o)∈_(rock) R _(rock))²]  (Equation 10)andimag(V/I)=−ω∈_(o) {ΔK _(mud)∈_(mud) R _(mud) ²/[1+(ω∈_(o)∈_(mud) R_(mud))² ]+K _(rock)∈_(rock) R _(rock) ²/[1+(ω∈_(o)∈_(rock) R_(rock))²]}  (Equation 11)

There may be five unknowns in these two equations R_(rock), ∈_(rock),R_(mud), ∈_(mud), and Δ. R_(rock) may be the property of interest thatis used to create a formation model. Therefore, if three of theseunknowns may be accounted for then R_(rock) may be calculated.

The measured impedance Z, the formation resistivity R_(rock) and the mudstandoff Δ may be frequency independent parameters. Therefore, thesefrequency independent parameters may correspond to two unknownparameters that are fixed at a particular logging point irrespective ofthe number of frequencies used. The formation permittivity ∈_(rock) mayalso be an unknown parameter. The unknown formation permittivity∈_(rock) may be included in the inversion. The formation permittivity∈_(rock) may be frequency dependent. Thus, the number of formationpermittivities ∈_(rock) to be inverted may be equal to the number ofoperating frequencies, or logging frequencies used. Alternatively, theinversion unit 510 may model the formation permittivity ∈_(rock) as apolynomial function of frequency or in terms of any other functionalform. Ideally we would like to have a minimum number of coefficients todescribe this frequency dependence. We can then invert for thesecoefficients instead of the formation permittivity ∈_(rock). One exampleof an inversion may be given as follows:∈_(rock) a ₁ +a ₂ω^(n) ¹ R _(rock) ^(n) ²   (Equation 12)

where a₁, a₂, n₁, n₂ may be unknown coefficients which may be found byperforming an inversion with the inversion unit 510. The number ofcoefficients may be fixed and therefore does not change with the numberof logging frequencies used. Therefore, the number of unknowns due tothe formation permittivity ∈_(rock) may not increase with the number offrequencies if the coefficients are determined by inversion.Alternatively, we may also consider that R_(rock) is frequency dependentand ∈_(rock) is frequency dependent, or that both are frequencydependent. The coefficients introduced to represent the frequencydependence can be inverted for by increasing the number of loggingfrequencies to make available a sufficiently large number of equations.

The downhole fluid properties, or mud properties, such as permittivityand conductivity, may also be frequency dependent, or function of thefrequencies. The mud properties may be directly inverted for at eachlogging frequency. Alternatively, the mud properties may be expressed asa polynomial function of frequency or in any other functional form witha minimum number of coefficients. These coefficients may be determinedby inversion using the inversion unit 510.

To determine the unknown parameters, or formation and/or downhole fluidproperties R_(rock), ∈_(rock), R_(mud), ∈_(mud), and Δ, the inversionunit 510 may perform an inversion of the formation data and/or the muddata. The inversion may be an iterative process where guesses for theunknown properties R_(rock), ∈_(rock), R_(mud), ∈_(mud), and Δ aresuccessively refined to reduce to a minimum the difference between themeasured current values and corresponding values computed from a forwardmodel, using as input the guessed values of the unknown parameters. Inone example, equation 9 is the forward model. The functions K_(mud) andK_(rock) may be specific to a particular downhole tool 104 (as shown inFIG. 1). To make inversion feasible, a forward model such as equation 9may be constructed that represents closely the behavior of the actualdownhole tool. Any suitable method of representing the behavior of thedownhole tool 104 may be used. For example, a finite element (FE)modeling may be used to compute the formation sensor current, and/or themud sensor current, for a particular downhole tool 104. The FE model maytake into account the geometry and frequency of the downhole tool, andthe materials used in its construction. It may also take into accountthe position of the downhole tool relative to the wellbore wall 130and/or the mud cake 132, the size of the wellbore 106 and the materialsinside and surrounding it. A large number of such FE simulations may bemade to populate a representative volume of (R_(rock), ∈_(rock),R_(mud), ∈_(mud), and Δ) space, for the logging frequencies concerned.These numerical data may then be represented in an analytic form, suchas equation 9 with the analytic functions K_(mud) and K_(rock). Usingthis inversion process, the formation resistivity R_(rock), or invertedformation resistivity, may be determined.

The downhole tool 104 electronics may be difficult to calibrate at ahigh operating frequency. Therefore impedance measurements might have asystematic drift in the in-phase or out-of-phase components. Thesystematic drifts may be part of the unknowns to be inverted by theinversion unit 510.

If the mud parameters are not directly measured, for example by the mudsensor 202 (as shown in FIGS. 2-4), the downhole fluid properties may beinverted for with the formation properties and/or the mud standoff. Inorder to invert for the downhole fluid properties the number offrequencies used in the plurality of currents 304A may be increased. Theincrease in frequencies may allow the inversion unit to determine theadditional unknowns created by the downhole fluid parameters beingunknown. The downhole fluid 108 (as shown in FIG. 1) remains fairlyconstant in the wellbore. Therefore, the inversion unit 510 may onlyneed to invert for the downhole fluid properties sporadically.Therefore, the increased number of frequencies and therefore, the numberof the plurality of currents 304A may only need to be increasedsporadically while logging. Further, the number of currents 304A usedmay be increased to allow the inversion unit to determine the mudproperties during the entire logging operation.

The formation model unit 512 may construct a formation model from theformation properties obtained by the inversion unit 510. The formationmodel may be any suitable model for determining formation propertiesand/or the location of valuable downhole fluids such as hydrocarbons.The formation model may be constructed based on the formationresistivity R_(rock). The formation model unit 512 may store,manipulate, and organize one or more formation models. The formationmodel may be an approximate model, or may be replaced by a tool modelderived using 3D modeling. The 3D model may be constructed using thedata from the inversion unit 510, for example the multi-frequencyparametric inversion, to obtain the formation resistivity from themeasured impedance.

The formation model may be constructed with one or more layer boundariesusing inverted formation properties from measurements taken at multiplelogging points in the wellbore 106 (as shown in FIG. 1). Thus, theformation model may be a homogeneous formation model at each loggingpoint in order to limit the number of model parameters. The homogeneousapproach may lead to uncertainty at or near the formation boundarieswhere the medium is not homogeneous. Therefore, a multi-layer formationmodel may be constructed by the formation model unit 512 to representthe formation. For the multi-layered formation model more parameters maybe inverted by the inversion unit 510. For example, each formation layermay have its resistivity, permittivity, boundary positions, layer dip,and/or layer azimuth inverted. The increased number of parameters to beinverted by the inversion unit 510 may require using measurements ofmultiple log points in the inversion.

The wellbore optimizer unit 514 may use the formation model and/or anyof the data stored in the formation imaging unit 118 to construct,optimize, change and/or create a well plan. The well plan may allow anoperator, controller and/or driller to optimize the production ofhydrocarbons from the wellsite. For example, the well plan may determinedrilling trajectories, location of multiple wellbores, drilling methods,completion methods, production methods, and the like. The wellboreoptimizer unit 514 may be an optional unit. Further, the wellboreoptimizer unit 514 may be located offsite.

FIGS. 6-11 are graphical depictions of various outputs that may begenerated by the formation imaging unit of FIG. 5. FIGS. 6 and 8-11 areplots of true resistivity (x-axis) versus reconstructed (inverted)resistivity (y-axis). FIG. 7 is a plot of formation resistivity (x-axis)versus signal strength (y-axis).

FIG. 6 depicts a comparison between the inverted formation resistivity600, as determined by the inversion unit 510, and a true formationresistivity 602. A line 604 represents the case when the invertedformation resistivities agree, almost exactly, with their true values.In this example, two logging frequencies were used and it is assumedthat the mud properties are known through a direct measurement by themud sensor 202 (as shown in FIG. 2). In this case, there are a total offour unknowns that include the formation resistivity R_(rock), twoformation permittivities ∈_(rock) (one for each frequency), and the mudstandoff Δ. Each frequency produces two measured data points, i.e., thein-phase and out-of-phase signals, thus resulting in four equationsemployed by the inversion unit 510.

In the example as shown in FIG. 6, the inversion was carried out onsynthetic data to which random noise was added. Assuming the measuredcomplex impedance is Z, we add noise in the following fashion,In phase signal=Re{Z}+∥Z|*ran*δ%  (Equation 13)Out of phase signal=Im{Z}+∥Z∥*ran*δ%  (Equation 14)

where ∥Z∥=√{square root over ([(Re{Z})²+(Im{Z})²]/2)}{square root over([(Re{Z})²+(Im{Z})²]/2)} and ran is a random number. −1<ran<1. As shownin FIG. 6, the formation resistivities R_(rock) may be determined usingthe inversion unit 510 reliably with two frequencies (for example 0.5and 40 MHz) provided the mud properties are known and the measurementsare noise-free. However, there is typically noise contaminating themeasured data. The inversion of the formation resistivity may becomeless reliable as the noise level increases. This may be true for lessresistive formations due to the impedance contribution from theformation being more or less directly proportional to the formationresistivity R_(rock).

FIG. 7 shows an output of the inversion unit 510 for synthetic data (ofthe measured impedance 700A-700D) as a function of the formationresistivity 702, shown on the horizontal axis. A smooth line 704 foreach of the measured impedances 700A-700D, represent the noise-free datawhile non-smooth curves 706 represent the same data after adding 2.5%random noise. The measured impedance 700A may represent an imaginaryimpedance at 40.0 MHz. The measured impedance 700B may represent a realimpedance at 40.0 MHz. The measured impedance 700C may represent animaginary impedance at 0.5 MHz. The measured impedance 700D mayrepresent a real impedance at 0.5 MHz. The real part of the measuredimpedances 700A-700D shows a distortion due to contamination by thenoise, especially for conductive formations. To correct this problem themeasurements may be performed at a higher frequency. As is shown in the40 MHz curves measured impedance 700A and 700B, in comparison with the0.5 MHz curves, 700C and 700D, a higher frequency of operation mayreduce the amplitude difference between the in-phase and out-of-phasesignals, especially for the conductive formations. The higher frequencymay reduce the effect of the added random noise, thus helping to improvethe inversion performed by the inversion unit 510.

The inversion unit 510 (as shown in FIG. 5) may have to invert for threemud coefficients when the downhole fluid parameters are not measured.The inversion unit 510 may further need to invert for the formationresistivity and the mud standoff in addition to the mud coefficients.The additional frequencies used with the plurality of currents 304A mayallow the inversion unit 510 to determine the mud parameters. Althougheach added operating frequency may provide two additional equations, itmay also introduce one unknown formation permittivity to be inverted.Table 1 (shown below) depicts the number of unknowns and the number ofequations that may be used as the number of operating frequencieschanges.

TABLE 1 Number of Frequencies Number of Unknowns Number of Equations 2 74 3 8 6 4 9 8 5 10 10

FIGS. 8-11 depict an example of inverted results, performed by theinversion unit 510 (as shown in FIG. 5), for each of the tabulated casesas shown in Table 1. The frequency range as shown, is between 0.5 and 40MHz, and the operating frequencies are selected uniformly on alogarithmic scale within this range. Although the frequency range isshown between 0.5 and 40 MHz any suitable frequency may be used. Asshown in FIGS. 8-11, the inverted resistivity 800 produced by theinversion unit 510 is shown on the vertical axis. A true resistivity 802is shown on the horizontal axis. The plotted line 804 may represent thetrue resistivity value, the plotted circles 806 may represent theinverted resistivity with a 0.0% noise. The plotted triangles mayrepresent the inverted resistivity with a 0.5% noise. The plotted dots810 may represent the inverted resistivity with a 2.5% noise. FIG. 8 mayrepresent an inversion using two frequencies and seven unknowns. FIG. 9may represent an inversion using three frequencies and eight unknowns.FIG. 10 may represent an inversion using four frequencies and nineunknowns. FIG. 11 may represent an inversion using five frequencies andten unknowns. As shown, the inverted resistivity produced by theinversion unit 510 may be substantially accurate when the formation 136is more resistive than about 5 ohms. The results become less accurate asthe formation 136 resistivity reduces and as the noise added to the dataincreases.

For the outputs shown in FIGS. 8-11, the inversion may beunderdetermined since the number of equations used is less than thenumber of unknowns to be inverted. FIGS. 9 and 10 show that when nonoise is added to the data, the inverted formation resistivity may besubstantially accurate down to 0.2 ohms. This may be due to themeasurements being most sensitive to the formation resistivity but lesssensitive to the rest of the parameters such as the mud properties.

Comparing all the outputs shown in FIGS. 8-11 from the inversion unit510 (as shown in FIG. 5), it is shown that three operating frequencies,or logging frequency, may allow for the most robust inversion results,when compared to the higher frequencies. However, increasing theoperating frequency, or logging frequency, range if possible may improvethe situation for conductive formations since the noise effect will bereduced as shown in FIG. 7.

FIG. 12 depicts a flow diagram 1200 illustrating a method for imagingproperties of at least one subterranean formation 136 in the wellbore106 (as shown in FIG. 1). The flow begins by deploying 1202 a downholetool into the wellbore. The downhole tool may be any of the downholetools described herein and may have the sensor pad 120 thereon. The flowcontinues by collecting 1204 formation data from a plurality of currentssent through the at least one subterranean formation, the plurality ofcurrents having at least two varying, or different, high frequencies.The flow continues by inverting 1206 at least a portion of the formationdata with a formation imaging unit and determining 1208 at least oneformation property with the formation imaging unit.

FIG. 13A is an example image of mud sensor impedance measured at twofrequencies in a well filled with oil-based mud using the imaging unitor system described herein. From left to right, the image showsamplitude of impedance measured at a first frequency, amplitude ofimpedance measured at a second frequency, phase of impedance measured atthe first frequency and phase of impedance measured at the secondfrequency. FIG. 13B is an image obtained after inversion of impedanceshown in FIG. 13A. The impedivity of the mud was measured separately forthe inversion. From left to right, the image shows formation resistivitymeasured at the first frequency, formation resistivity measured at thesecond frequency, formation relative permittivity and standoff.

While the embodiments are described with reference to variousimplementations and exploitations, it will be understood that theseembodiments are illustrative and that the scope of the inventive subjectmatter is not limited to them. Many variations, modifications, additionsand improvements are possible. For example, additional sources and/orreceivers may be located about the wellbore to perform seismicoperations.

Plural instances may be provided for components, operations orstructures described herein as a single instance. In general, structuresand functionality presented as separate components in the exemplaryconfigurations may be implemented as a combined structure or component.Similarly, structures and functionality presented as a single componentmay be implemented as separate components. These and other variations,modifications, additions, and improvements may fall within the scope ofthe inventive subject matter.

What is claimed is:
 1. A formation imaging unit for imaging propertiesof at least one subterranean formation in a wellbore at a wellsite, theformation imaging unit comprising: a current management unit forcollecting data from at least two currents injected into the at leastone subterranean formation, the at least two currents having at leasttwo different frequencies; a drilling mud data unit for determining atleast one drilling mud parameter; a formation data unit for determiningat least one formation parameter from the collected data; and aninversion unit for determining at least one formation property byinverting the at least one formation parameter, wherein the at least oneformation property is determined by inverting the drilling mud parameterand the at least one formation parameter, and wherein a sensor standoffis determined by the inversion unit.
 2. The formation imaging unit ofclaim 1, wherein the at least two currents comprise at least threecurrents.
 3. A system for imaging properties of at least onesubterranean formation in a wellbore at a wellsite, the systemcomprising: a formation sensor for collecting at least two currentsinjected into the at least one subterranean formation, the formationsensor positionable on a downhole tool deployable into the wellbore; amud sensor for collecting at least one current injected into a boreholemud fluid, wherein the at least one current injected into the boreholemud fluid has the same frequency as one of the at least two currentsinjected into the at least one subterranean formation a controller forcontrolling the formation sensor; a formation imaging unit, theformation imaging unit comprising: a current management unit forcollecting data from the at least two currents injected into the atleast one subterranean formation, the at least two currents having atleast two different frequencies; a drilling mud data unit fordetermining at least one drilling mud parameter; a formation data unitfor determining at least one formation parameter from the collecteddata; and an inversion unit for determining at least one formationproperty by inverting the at least one formation parameter.
 4. A methodfor imaging properties of at least one subterranean formation in awellbore at a wellsite, the method comprising: deploying a downhole toolinto the wellbore, the downhole tool having a formation sensor thereon;collecting at least three currents sent through the at least onesubterranean formation from the formation sensor and inverting theformation parameters collected by the three currents and inverting forthe drilling fluid parameters; sending formation data from the at leasttwo currents to a formation imaging unit, the formation imaging unitcomprising: a current management unit for collecting data from the atleast two currents injected into the at least one subterraneanformation, the at least two currents having at least two differentfrequencies; a drilling mud data unit for determining at least onedrilling mud parameter; a formation data unit for determining at leastone formation parameter from the collected data; an inversion unit fordetermining at least one formation property by inverting the at leastone formation parameter; and determining at least one formation propertywith the formation imaging unit.
 5. The method of claim 4, furthercomprising determining a formation resistivity by inverting theformation parameters, the drilling fluid parameters and a sensorstandoff.